(497b) Dynamic Real-Time Optimization of Distributed MPC Systems Using Rigorous Closed-Loop Prediction

Dynamic real-time optimization (DRTO) has been developed as a supervisory layer within the process control architecture that computes set-point trajectories for an underlying regulatory control system based on economic optimization and a dynamic process model. Unlike traditional steady-state RTO systems, it does not require the plant to be at steady state prior to execution, thus making it well-suited for systems with recycle, with slow dynamics and which undergo frequent grade changes. Tosukhowong et al. propose a DRTO formulation to capture slow dynamics of a system using a linear model [1], while Kadam and Marquardt develop a DRTO formulation that estimates uncertain parameters and performs fast updates based on a sensitivity technique [2]. Most DRTO systems are based on an open-loop model of the process that does not consider the dynamic effects of the underlying regulatory controller. However, DRTO formulations based on the closed-loop prediction of the plant under constrained MPC have recently been developed [3, 4].

Large process plants are generally not controlled using a single, monolithic MPC system, with a distributed MPC architecture favored to take the modularity of a large process into consideration and provide additional flexibility [5]. Thorough reviews on the architecture and formulations of distributed MPCs have been conducted in [6, 7, 8]. Camponogara et al. propose a coordination scheme that allows communication among MPC subsystems which is allowed once for each local problem and multiple times before implementation of the control actions [9]. Liu et al. introduce distributed Lyapunov-based MPCs that adopt a sequential and iterative approach with one or bi-directional strategies, under the assumption of known state feedback for all controllers [10]. Stewart et al. present a cooperative scheme for distributed MPCs that ensures the closed-loop stability of the system upon termination of iterations for all subsystems [11].

In this work, a closed-loop DRTO formulation is developed for the economic coordination of distributed MPC systems by assigning computed set-point trajectories based on the prediction of future interactions between the plant dynamics and distributed MPCs. This closed-loop formulation naturally results in a multilevel optimization problem whose primary optimization problem computes the reference trajectories for each MPC subsystem based on a full plant dynamic model under an economic objective, and whose MPC optimization sub-problems compute optimal control actions to be applied to the full plant dynamic model based on partial models each of which contains model equations relevant to its associated subsystem. Such a multilevel optimization problem can be transformed into a single-level optimization problem by applying the Karush-Kuhn-Tucker (KKT) optimality conditions to transform the MPC optimization sub-problems into sets of algebraic constraints embedded in the primary optimization problem, resulting in a single mathematical program with complementarity constraints (MPCC).

Relevant linear and nonlinear case studies are conducted to explore two modes of operation of the DRTO formulation: target tracking and economic optimization. Results show that for economic optimization, due to the flexibility of set-point trajectories and ability to foresee future interactions, the closed-loop DRTO formulation has the capacity to coordinate distributed MPCs to achieve similar economic performance when compared to the centralized counterpart, and for target tracking, each output is able to achieve the desired target value rapidly compared to both centralized and decentralized MPC cases.

Due to the large scale and level of detail modeled for each subunit of a process, approximation techniques for the closed-loop DRTO formulation would be useful in order to efficiently coordinate multiple distributed MPCs at various locations. Strategies of this type are under development, with economic and computational performance comparisons planned.

References

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